Density-functional theory of pair correlations in metallic hydrogen

Abstract

The pair correlations in the metallic phase of hydrogen are reconsidered on the basis of a simple density-functional formulation of the free energy of the ion-electron plasma, which includes a square-gradient correction to the Thomas-Fermi kinetic energy of the degenerate electrons. A robust prescription is given for the prefactor of the square-gradient correction. The functional leads to a hypernetted-chain--like closure for the ion-ion and ion-electron correlation functions, which is solved iteratively, in conjunction with the coupled Ornstein-Zernike equations relating the matrices of pair and direct correlation functions. The resulting structure agrees well with available ab initio simulation data based on the Kohn-Sham functional. A density- and temperature-dependent effective ion-ion pair potential is obtained by formally reducing the initial two-component system to a one-component fluid of pseudoatoms. The results show strong deviations of the present nonlinear theory from the standard linear screening approach for ${r}_{s}>1$ (where ${r}_{s}$ is the usual inverse density parameter equal to the ratio of the electron sphere radius over the Bohr radius). The long-wavelength ion density fluctuations are strongly enhanced as the density drops, and at the lowest density ${(r}_{s}=1.5)$ the ion-ion pair structure and effective potential exhibit an unusual behavior, at the lower temperature explored in this paper $(T=3\ifmmode\times\else\texttimes\fi{}{10}^{3}\mathrm{K}),$ which may be interpreted as a precursor to an incipient plasma-insulator transition. Thermodynamic properties are estimated from the pair structure. The influence of nonlinear electron polarization on the equation of state is found to be surprisingly small, but the isothermal compressibility increases sharply at the lowest density.